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Brooklyn’s Republican and Conservative party leaders want veteran DA Charles “Joe” Hynes to actively campaign to hold on to his office.

Hynes, 78, was upset by Kenneth Thompson in last week’s Democratic primary, but Hynes’ name will still appear on the other two lines.

He’s indicated he won’t campaign, but GOP and Conservative sources claim that if he did, Hynes could add enough Democratic votes to put him over the top.

GOP mayoral candidate Joe Lhota is among those urging Hynes to campaign, the sources said. Lhota declined to comment.

“Crime is down. Murders are way down. Hynes has gotten the scum of the earth off the street,” said Brooklyn GOP state Sen. Marty Golden.

“People woke up and were shocked Hynes lost the primary. People woke up and said, ‘This is not the change we wanted.’ Many Democrats felt bad they didn’t come out and vote for him. But they will in the general election.”

If Hynes gives the green light, Golden said, he could get enough financial support to campaign.

State Conservative Party Chairman Mike Long said Brooklynites he’s spoken to are in Hynes’ corner.

“Many people will vote for Hynes on the Republican and Conservative lines,” Long said. “It’s not impossible that he could pull out a victory.”

After the repudiation by his own party, Hynes said he wouldn’t actively campaign in the general election. He congratulated Thompson and agreed to help pave the way for a smooth transition.

But on Friday, he told The Post he was “flattered to hear that many supporters are attempting to raise money to convince me to run for re-election on the Republican and Conservative lines.”

Hynes’ allies point out that only about one in five registered Democrats voted in the primary.

But Team Thompson is taking Hynes at his word.

“Ken Thompson . . . is looking forward to a smooth transition, as was discussed with outgoing DA Hynes,’’ said Thompson spokesman James Freedland.

Still, the Hynes camp is troubled by a Post report last week that disgraced ex-Brooklyn Democratic Party boss Clarence Norman — whom the DA convicted for pay-to-play corruption in 2007 — helped Thompson and showed up to celebrate at the winner’s victory party, said Hynes’ campaign chairman’ Dennis Quirk.

Thompson and his aides repeatedly denied that Norman played any role in the campaign.